Brant Jones

Department of Mathematics and Statistics
MSC 1911
James Madison University
Harrisonburg, VA 22807

email: jones3bc (a t) jmu (d o t) edu

office: 325 Roop Hall, 540 568.3802


I am an Associate Professor at James Madison University. I studied mathematics (and electronic music) as an undergraduate at Bard College and went to work as a software developer and consultant at PricewaterhouseCoopers in the late 1990s. After returning to school, I earned my Ph.D. in mathematics in 2007 from the University of Washington in Seattle, and was selected for a postdoctoral VIGRE Fellowship at the University of California, Davis for three years before moving to Virginia.

Since joining JMU, I've mentored several undergraduate research projects for students majoring in math and computer science, both locally as well as part of the NSF REU site that we host during the summer. In 2013, I was invited to participate as a visiting researcher in the semester program on Combinatorial Representation Theory at the Institute for Computational and Experimental Research in Mathematics (ICERM).

My research interests include algorithms, algebraic structures, and enumerative combinatorics, particularly as related to the representation theory of reflection groups.


Teaching

I have been awarded a sabbatical semester for Fall 2016. Some of my previous classes include:

  • Nature of Mathematics Math 103
  • Discrete Structures CS/Math 227
  • Calculus (with Functions) Math 231
  • Calculus I Math 235
  • Calculus II Math 236
  • Calculus III (Multivariable) Math 237
  • Discrete Mathematics Math 245
  • History of Mathematics Math 415
  • Abstract Algebra I Math 430
  • Abstract Algebra II Math 431
  • Advanced Linear Algebra Math 434
  • Putnam Problem Solving Seminar Math 485 (usually with Dr. Rebecca Field)


Some Papers Especially For or By Undergraduate Researchers

Rational generating series for affine permutation pattern avoidance

The Refined Lecture Hall Theorem via Abacus Diagrams   (with Laura Bradford, Meredith Harris, Alex Komarinski, Carly Matson, and Edwin O'Shea)

Solitaire Mancala Games and the Chinese Remainder Theorem   (with Laura Taalman and Anthony Tongen)

Permutations, Pattern Avoidance, and the Catalan Triangle   (with Derek Desantis, Rebecca Field, Wesley Hough, Rebecca Meissen, and Jacob Ziefle)
Missouri Journal of Mathematical Sciences 25 (1) (2013) 50-60    preprint version


Additional Publications (with descriptions)

Results and conjectures on simultaneous core partitions   (with Drew Armstrong and Christopher R. H. Hanusa)

Using carry-truncated addition to analyze add-rotate-xor hash algorithms   (with Rebecca Field)

Mask formulas for cograssmannian Kazhdan--Lusztig polynomials   (with Alexander Woo)

Abacus models for parabolic quotients of affine Weyl groups   (with Christopher R. H. Hanusa)

Affine structures and a tableau model for E6 crystals   (with Anne Schilling)

The enumeration of maximally clustered permutations   (with Hugh Denoncourt)

The enumeration of fully commutative affine permutations   (with Christopher R. H. Hanusa)

An explicit derivation of the Möbius function for Bruhat order  

A bijection on core partitions and a parabolic quotient of the affine symmetric group   (with Chris Berg and Monica Vazirani)

Leading coefficients of Kazhdan--Lusztig polynomials for Deodhar elements  

Kazhdan--Lusztig polynomials for maximally-clustered hexagon-avoiding permutations  

Embedded factor patterns for Deodhar elements in Kazhdan-Lusztig theory   (with Sara C. Billey)


Mathematical Software

Sage: I have contributed some code to sage.combinat, particularly an initial implementation of the Lenart--Postnikov alcove path model for crystals.

liberiksson: A C++ library to perform fast computations on elements of Coxeter groups, used for some of my papers on Kazhdan--Lusztig polynomials. More specifically, the code classifies the Deodhar elements of finite Coxeter groups by embedded factor containment, and verifies that the mu coefficients for Kazhdan--Lusztig polynomials associated to these elements are always 0 or 1.


Erdős number:    3